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Author ORCID Identifier
N/A
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2018
Month Degree Awarded
September
First Advisor
Andrea R. Nahmod
Subject Categories
Analysis | Partial Differential Equations
Abstract
This thesis studies the cubic nonlinear Sch\"rodinger equation (NLS) on tori both from the deterministic and probabilistic viewpoints. In Part I of this thesis, we prove global-in-time well-posedness of the Cauchy initial value problem for the defocusing cubic NLS on 4-dimensional tori and with initial data in the energy-critical space $H^1$. Furthermore, in the focusing case we prove that if a maximal-lifespan solution of the cubic NLS \, $u: I\times\mathbb{T}^4\to \mathbb{C}$\, satisfies $\sup_{t\in I}\|u(t)\|_{\dot{H}^1(\mathbb{T}^4)}
DOI
https://doi.org/10.7275/12530737
Recommended Citation
Yue, Haitian, "WELL-POSEDNESS FOR THE CUBIC NONLINEAR SCHRÖDINGER EQUATIONS ON TORI" (2018). Doctoral Dissertations. 1394.
https://doi.org/10.7275/12530737
https://scholarworks.umass.edu/dissertations_2/1394